The stability problem of the functional equation was conjectured by Ulam 1 during the conference in the University of Wisconsin in 1940. In the next year, it was solved by Hyers 2 in the case of additive mapping, which is called the Hyers-Ulam stability. Thereafter, this problem was improved by Bourgin 3 , Aoki 4 , Rassias 5 , Ger 6 , and Gǎvruţa et al. 7, 8 in which Rassias’ result is called t...

‎The aim of this paper is to introduce and solve the‎ radical cubic functional equation‎ ‎$‎‎fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)‎$.‎ ‎We also investigate some stability and hyperstability results for‎ ‎the considered equation in 2-Banach spaces‎.

Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.